An improved method of removing the residues of fabrication from carbon nanotubes has been invented. These residues comprise amorphous carbon and metal particles that are produced during the growth process. Prior methods of removing the residues include a variety of processes that involved the use of halogens, oxygen, or air in both thermal and plasma processes. Each of the prior methods entails one or more disadvantages, including non-selectivity (removal or damage of nanotubes in addition to removal of the residues), the need to dispose of toxic wastes, and/or processing times as long as 24 hours or more. In contrast, the process described here does not include the use of toxic chemicals, the generation of toxic wastes, causes little or no damage to the carbon nanotubes, and involves processing times of less than 1 hour. In the improved method, purification is accomplished by flowing water vapor through the reaction chamber at elevated temperatures and ambient pressures. The impurities are converted to gaseous waste products by the selective hydrogenation and hydroxylation by the water in a reaction chamber. This process could be performed either immediately after growth or in a post-growth purification process. The water used needs to be substantially free of oxygen and can be obtained by a repeated freeze-pump-thaw process. The presence of oxygen will non-selectively attach the carbon nanotubes in addition to the amorphous carbon.